Ask Ars: Why spend time and money finding new prime numbers?

That new 17-million digit Mersenne prime number might matter. Someday.

Are we wasting computer power looking for new numbers with certain properties?

In 1998, Ask Ars was an early feature of the newly launched Ars Technica. Now, as then, it's all about your questions and our community's answers. We occasionally dig into our question bag, provide our own take, then tap the wisdom of our readers. To submit your own question, see our helpful tips page.

OK, you've got us. The jig is up. There is no use for absurdly large prime numbers—yet (we’ll explain that eventually). Slightly less ludicrous prime numbers do have a point, which we'll describe here.

One modern-day instance of practical use for prime numbers is in RSA encryption, which allows two parties to pass secret messages back and forth using independent encryption and decryption codes. In RSA, someone who wants to receive a private message will publish a product of two large prime numbers as their "public key," which senders can use to encrypt messages intended for the key publisher.

The publisher is able to decrypt the encrypted messages using the two prime numbers that are the factors of the product she published; the presumption is that an interloper won't be able to decode it because factoring the product of the two primes is time-consuming and tiresome, and trying to find the right prime numbers that created the product would be tough. The bigger the prime numbers used, the more possible combinations there are to create the public key and the harder it is to find the right combination.

In reality, there is more computation involved. Encrypting with the public key involves choosing a number unknown to the message recipient (or anyone else) and performing calculations with it that can only be undone by the recipient, because she knows the key prime numbers. Ars has a rundown of the theoretical RSA process, and Wikipedia has a nice example of how RSA encryption works using relatively small prime numbers.

But the significance of the keys' basis in two prime numbers is that there can be no confusion about the factorization. If the key were based on a product of any two numbers, there might be many combinations of integers that could generate the key. Because primes are indivisible by numbers other than one and themselves, the division possibilities are finite.

The larger the product of the two prime numbers is, the more prime numbers an interloper would have to try to break the code. We do need sufficiently big prime numbers for this, and as the computers of the evil mustache-twirlers of the world become more powerful, we need bigger primes all the time.

A Mersenne prime, which is the type of prime number that was discovered in late January, is one that can be expressed in the form 2n-1. The point of this expression is that, for every Mersenne prime, there is a corresponding perfect number, an integer that is both the sum and product of its factors—6 is an example (1*2*3 or 1+2+3). The perfect number related to a Mersenne number can be expressed in a slight rearrangement of the Mersenne prime's formula: 2n-1(2n-1). What's the point of a perfect number? There is none, practically; numerologists and other ancient cultures considered them mystical and significant, but in the modern-day they're just kind of neat.

If a prime number, even a large one, is useful in the way that a four-door sedan is useful, the prime number discovered last week is a four-door sedan that is a hundred feet tall, five hundred feet long, and gets .000001 miles to the gallon. It might be useful to someone (or something), someday, but it is not useful to you, here, now.

Why we bother

In modern-day computing, prime numbers can sometimes be about the journey, not the destination. For instance, a program called Prime95 can be used to search for Mersenne prime numbers, but it also became popular for testing the stability of a system among people who stress-test hardware and overclock processors. Because the important aspect here is search, not discovery, it doesn't matter if the program finds a new prime number while stress-testing (it won't, since it only needs to run for a set number of hours before the system it's on can be deemed stable). The important part is the strain.

The search for prime numbers, given a certain amount of intensity, is easy to construct. To be overly simplistic about it, the workflow is something like this: take a number, start dividing it by numbers lower than it until one works, rinse and repeat (and do it quickly, please).

But that task becomes increasingly difficult as the starting numbers get higher. Perhaps prime number factorization, come the singularity, could be weaponized against the Cylons. It's the computer equivalent of asking someone to move the Sahara Desert's sand to lower Africa; they might find some rare minerals or artifacts along they way, but that's not why you asked them to do it. You just wanted to see if they could move a desert’s worth of sand.

Not much harm comes of seeking larger prime numbers, so long as you don't consider the use of spare calculating power put toward the search for prime numbers to be a waste. The Great Internet Mersenne Prime Search (GIMP) is done by computers set up to search in their spare time, and they chip away at it slowly. Only four new Mersenne primes have been found by GIMP in the last five years.

But even "pointless exercises" can have surprising payoffs. Throughout most of their history, prime numbers have had little productive use other than building the foundations of theoretical mathematics. Then RSA cryptography was developed in 1977, giving us an extremely robust method for passing secret transmissions that only worked because of the fundamental properties of prime numbers. In a similar vein, when Einstein first described a theory of relativity, no one could do much with it until we developed more tools to observe how the Universe works on a large scale. Now, relativity comes in very handy.

Much theoretical research has no apparent point except to serve as a building block for more theoretical research, but when something turns out to be practically useful, scientists are glad to have it.

Promoted Comments

Why bother finding new prime numbers? The question really is of the form:

Why bother being interested in ${X} when it has no practical use at the present time ${Y}.

Do you know how how many values of X there are at past times of Y?

In 1905 and 1915 why is special and general relativity important? The examples Einstein constructed use choo-choo trains instead of spaceships, which shows how irrelevant both versions of the theory was to everyday life. Today, GPS works because it is corrected for relativity.

Why have an interest in quantum mechanics about one hundred years ago? What practical use could it have? Today we would not have transistors (1950's) and integrated circuits that make all our fun toys possible, including how you are reading this right now.

Why have any interest in prime numbers centuries ago? What possible use could it have. Of course, you find it important every time you use an SSL web site whose url starts with HTTPS or when you buy something online, say at Amazon.

At one point, the phenomena of static electricity, inducing currents in a wire with magnets, creating a magnetic field with a coil of wire with a current in it, were just cute parlor tricks for amusement. Stunts. Much like the stunts of calculating pi to absurd lengths, or finding ever larger prime numbers.

It may not be useful today. It may never be useful. Or it may be extremely useful, but not today. It might even be extremely useful later, but not in our lifetime.

So when someone suggests that such things are a waste, I feel quite safe ignoring them.

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

It may be helpful to point out that the prime numbers used in RSA keys are very small compared to the Mersenne prime discovered, 4096 bit RSA keys use approximately 616 digit prime numbers, while the discovered Mersenne prime has over 17 million digits.

What's wrong with "because scientific research for its own sake, even without a direct practical application, is awesome"?

You can never predict where the next momentous discovery will come from, and more often than not it's not at all what the researchers were intending. (see also: cosmic microwave background radiation.) Sure the chance of a world-changing discovery coming from finding huge prime numbers is pretty slim, but "slim" is greater than zero, which is really all that matters.

Why bother finding new prime numbers? The question really is of the form:

Why bother being interested in ${X} when it has no practical use at the present time ${Y}.

Do you know how how many values of X there are at past times of Y?

In 1905 and 1915 why is special and general relativity important? The examples Einstein constructed use choo-choo trains instead of spaceships, which shows how irrelevant both versions of the theory was to everyday life. Today, GPS works because it is corrected for relativity.

Why have an interest in quantum mechanics about one hundred years ago? What practical use could it have? Today we would not have transistors (1950's) and integrated circuits that make all our fun toys possible, including how you are reading this right now.

Why have any interest in prime numbers centuries ago? What possible use could it have. Of course, you find it important every time you use an SSL web site whose url starts with HTTPS or when you buy something online, say at Amazon.

At one point, the phenomena of static electricity, inducing currents in a wire with magnets, creating a magnetic field with a coil of wire with a current in it, were just cute parlor tricks for amusement. Stunts. Much like the stunts of calculating pi to absurd lengths, or finding ever larger prime numbers.

It may not be useful today. It may never be useful. Or it may be extremely useful, but not today. It might even be extremely useful later, but not in our lifetime.

So when someone suggests that such things are a waste, I feel quite safe ignoring them.

I highly recommend the NumberPhile channel on youtube, they just had a video on perfect numbers, Mersenne Primes, and this newly discovered prime. Their videos aren't overly technical, and it's cool to see people who are so enthusiastic about math and science.

I urge anyone to invest heavily in my quest to figure out what the biggest edible structures is that can be made out of vast amounts of gummi bears. Obviously with this research I need quite a lot of money for the bears alone, not including housing, expenses, utilities etc. Sure, it may seem wasteful and pointless now, but this research might be the foundation of incredible scientific breakthroughs in the future. You never know.

I highly recommend the NumberPhile channel on youtube, they just had a video on perfect numbers, Mersenne Primes, and this newly discovered prime. Their videos aren't overly technical, and it's cool to see people who are so enthusiastic about math and science.

I second this recommendation. I stumbled upon the Numberphile channel a few weeks ago when I was just mindlessly clicking on videos. Lots of interesting videos on math and numbers presented in a way just about anyone can understand. If you liked Numberphile you may also like Brady Haran's other channel about chemistry, Periodic Videos

I urge anyone to invest heavily in my quest to figure out what the biggest edible structures is that can be made out of vast amounts of gummi bears. Obviously with this research I need quite a lot of money for the bears alone, not including housing, expenses, utilities etc. Sure, it may seem wasteful and pointless now, but this research might be the foundation of incredible scientific breakthroughs in the future. You never know.

The size of such structures would be influenced by gravity. In a location with lower gravity, larger structures could be built. This is because the material you are using to construct the structures has a fixed strength. Therefore in any specific gravitational field, there will be a natural upper limit to the size of structures you can construct.

It should be a relatively simple, short and relatively inexpensive research project.

A logical extension would be that with different construction materials, what is the natural upper limit in any particular gravity? What if you used Oreo cookies. Cans of diet coke. Steel. Granite. Reinforced concrete. Etc. In Earth's gravity you could have a table of materials vs. natural upper limit on structure. You could extend this to a table of formula that lets one calculate the upper limit for any given gravity, for each type of material.

Good luck with your research. But I suspect the useful results are already fairly well known. If it becomes useful to know the answer for gummi bears, I suspect the question will be answered relatively quickly.

In general, the kind of seemingly impractical research that tends to have a more likely chance of being useful later is usually related to phenomena of nature.

I urge anyone to invest heavily in my quest to figure out what the biggest edible structures is that can be made out of vast amounts of gummi bears. Obviously with this research I need quite a lot of money for the bears alone, not including housing, expenses, utilities etc. Sure, it may seem wasteful and pointless now, but this research might be the foundation of incredible scientific breakthroughs in the future. You never know.

Has anyone done any studies on how much energy is being used doing things like this, in spare computer time?

THEY HAVE NOW

Assumptions: most people are now using computers of the Core2 generation or newer, which idle using substantially less power than they use to run flat-out. Say 20 watts per core difference between idle and flat-out (Core2 figure was about 25, Ivy Bridge about 15W) and average three cores per computer because the machines are biased towards enthusiasts with four-core setups. Call it 60W per computer.

So about $600,000 a year on electricity that would not be used were the machines actually idling when inactive.

For comparison, a driver bug or a bug in a virus-checker that stops 1% of the US computer population from idling when inactive would cost a hundred times as much, since well under 0.01% of the computers in the US are contributing to primenet.

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

You can never predict where the next momentous discovery will come from, and more often than not it's not at all what the researchers were intending

You say this, but it's not entirely obvious that it's true, particularly not in the post-WW2 environment of Big Science, and particularly not in well-understood fields like mathematics.

There are always technological spin-offs when you find that you have to switch to industrial-scale production of something that was previously a laboratory curiosity: ubiquitous MRI machines exist because Fermilab needed miles of superconducting cable, so people manufactured miles of superconducting cable, so the machinery was available to make further miles of superconducting cable for the MRI machines.

I've seen descriptions of the history of the CCD which focus on their early use for astronomy, though there is clearly a lot of DoD usage which occurred even earlier and is unlikely to be documented for another twenty years.

I'm a researcher in computer science, with an interest forelementary number theory and a truly passion for recreational mathematics,which occupies a very good part of my spare time.I also totally support base research.

However, I'm not very impressed by these results.Let me explain my point of view.

Apart being prime, and big, there is nothing really interesting in the discover of further Mersenne primes. They are just big primes of a specific form.The properties of Mersenne numbers are interesting.The discovery of a specific such number, on the contrary, tells nothing new to mathematicians.

One may object that this numbers may be useful or interesting in thefuture. I agree, so I'm in favor of studying new mathematical techniquesto find them more easily. So, if in the future we discover that they are important,we can find them faster. On the other side, simply using current techniques over thousandsof CPUs for finding a number which is nothing more than a curiosity,seems to me a waste. Since I like recreational math, I would prefer to use a fraction of that cpu powerto search for other kind of (almost surely useless) numbers which I find moreinteresting. ;-)

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

"You don't know what you don't know"

I think the article was on Ars a couple weeks back that basically said that the odds of discovering some breakthrough on the scale of breaking the atom or theory of relativity were becoming less and less by the day. It also said that because of those odds, people are focusing research on more highly specialized areas, mostly because thats where the money is.

With that trend of focusing, I would argue that we need research for research's sake more than ever, otherwise we may never learn something truly new. I won't go so far as to call counting grains of sand valid, but just about any research in math (which can be applied to just about anything) is likely to pay off at least somewhere down the road.

I'm a researcher in computer science, with an interest forelementary number theory and a truly passion for recreational mathematics,

One may object that this numbers may be useful or interesting in thefuture. I agree, so I'm in favor of studying new mathematical techniquesto find them more easily. So, if in the future we discover that they are important,we can find them faster.

And indeed that's something that the search for large Mersenne numbers has encouraged; without having the big primes as a goal, I suspect the discrete-weighted-transform would not have been developed, and I suspect Woltman would not have written the series of superbly optimised fast Fourier transforms (about twice the speed of FFTW!) which Prime95 uses.

This means that extremely sharp and convenient tools are available if anyone wants to do recreational mathematics with big (millions of digit) numbers nearly all of whose digits in some base are the same, and a lot of them can be used for big numbers in general.

There are surprisingly many cases where efficient multiplication of million- to billion-digit numbers comes in useful; recently, it was the essential tool behind all the papers on how consumer devices were using inadequate entropy sources and generating easily breakable RSA keys for SSL.

It's another example of developing a general-purpose technology which you aimed at a particular problem and the rest of the world can aim at their own.

The point is not only that finding marsenne primes has no practical application, but that it has no theoretical benefit either. In other words, there is no number theorist out there saying, "finally, they have found 2^123456... -1, I can finally prove my theory."

True, Prime95 is one way to stress test a cpu. Running it for thousands of hours on thousands of machines is still a waste of electricity. True, RSA encryption needs large primes, but they do not need to be that large, or marsenne. If the time ever comes when we need specific marsenne primes, we can search for them using future, better CPUs.

I'll say it again, if you want to donate spare cycles, you can help cure Alzheimer's at folding@home.

The article badly under-rates the value of prime numbers. Of any size.

The truth is, if you take any sort of number theory course, they turn up over and over again.

So does "the prime factorization" of composite numbers. It's just and important and fundamental property of numbers that sooner or later is going to find uses. Learning more about them is likely to pay off, sooner or later.

In fact, they are arguably under-used. I've used primes in my professional work many times to obtain some rather mundane robustness advantages. It turns out you sometimes get better results if two supposedly independent processes actually do function more independently.

If you use prime numbers for some key, otherwise arbitrary constants, you avoid various resonance effects that in some way (perhaps merely performance, perhaps a little bit functionally) make some pair of process less independent of each other in practice.

1. Prime numbers are the building blocks of all numbers and number theory.2. Mathematicians know embarrassingly about what constitutes a prime number.3. We can recognize a prime number with some work, but we can't, for instance, predict where along a number line or how many times a prime will show up in a given range (exactly, which is, again, embarrassing).4. Mersenne primes represent one avenue of rectifying this, since prediction models tend to break down faster and more visibly at extreme ranges, allowing us to refine and develop new understandings of primes.5. Z-space understanding depends on prime numbers, and even if you don't know what that is, it sounds so freaking cool why shouldn't we invest time and money on it?

There's also the obvious application of using the search for prime numbers to advance the state of the art in numerical analysis and distributed processing by creating pressure to develop better algorithms and workflows. That in turn benefits any field that relies heavily on numerical analysis (climate modeling, economic forecasting, physical simulations, etc).

Snark aside, what I'm trying to say is that we (as a species) tend do what pleases us.

And I'm really not arguing against that.

I'm just saying that the follow up of "Well, why are you doing that?" is fair game.

Many here seem to think that we shouldn't even ask the question. By all means, do whatever you want. But I defend the necessity of asking you "why?"

If we applied the sort of scrutiny to our lives that some folks think should apply to this kind of scientific research, we'd all be a lot less happy. People enjoy doing lots of things that aren't completely rational, which would fall apart under the slightest bit of "what can it do for the human race".

Unless you would enjoy nutritious gruel every day, no hobbies or entertainment of any kind, everyone living in uniform apartments with no decoration, no sports or art or vacations and on and on...

Sort of puts spending a few grand on electricity for a little wishful scientific thinking in perspective. THink of it as a hobby which has a slightly nonzero chance of being useful.

Donating computer time in and of itself is admirable, so I don't think folks should get into a pissing contest over which project they donate too.

However, I am of the same mind-set. I figured if we did things like cure cancer, helped folks live longer, etc, then there would be more human potential to put towards other problems.

But, who knows ... maybe finding large prime numbers helps cure cancer in the future, or prevent it easier or provides the key to immortality. Sometimes that solution to a problem occurs in a round-about fashion.

In the mean-time, I'll still crunch for world community grid's projects for humanity.

Out of all of it, my biggest concern in picking a project is ensuring that it's open ... ie: the results are considered public domain, not sequestered away by some business that will patent or copyright it for years to come.

If we applied the sort of scrutiny to our lives that some folks think should apply to this kind of scientific research, we'd all be a lot less happy. People enjoy doing lots of things that aren't completely rational, which would fall apart under the slightest bit of "what can it do for the human race".

Some of you are placing far too much gravitas into what I said. I never meant to imply that all actions must benefit humanity.

To be clear, I would accept "Because it makes me happy" as a legitimate answer to the "why?" question.

Why are you watching TV? ...counting sand? ...finding prime numbers?

"It makes me happy" an acceptable answer to all of those. I'm not dictating the answer. I'm rejecting the notion that asking is inappropriate.

1. Prime numbers are the building blocks of all numbers and number theory.2. Mathematicians know embarrassingly about what constitutes a prime number.3. We can recognize a prime number with some work, but we can't, for instance, predict where along a number line or how many times a prime will show up in a given range (exactly, which is, again, embarrassing).4. Mersenne primes represent one avenue of rectifying this, since prediction models tend to break down faster and more visibly at extreme ranges, allowing us to refine and develop new understandings of primes.5. Z-space understanding depends on prime numbers, and even if you don't know what that is, it sounds so freaking cool why shouldn't we invest time and money on it?

I don't think people disagree that prime numbers are useful. What's being argued is the value of finding this one particular prime number. As someone already said, this offers no theoretical benefit to our knowledge of prime numbers. So while everything you said is true, you only justified developing better theory for prime numbers, not aimlessly finding bigger ones. In general I don't think the brute force approach of trying all numbers and seeing what sticks is a good way to advance the field of mathematics.

The article also brought up relativity as an example of seemingly useless pursuit until it became useful - you might notice that it's because Einstein developed a *theory* around the subject, not because he spent thousands of hours manually correcting the redshift of every photon he captured. Again there's a huge difference between studying phenomena and discovering new theories, versus doing repetitive calculations on more and more objects using methods we already know about.

Donating computer time in and of itself is admirable, so I don't think folks should get into a pissing contest over which project they donate too.

However, I am of the same mind-set. I figured if we did things like cure cancer, helped folks live longer, etc, then there would be more human potential to put towards other problems.

But, who knows ... maybe finding large prime numbers helps cure cancer in the future, or prevent it easier or provides the key to immortality. Sometimes that solution to a problem occurs in a round-about fashion.

In the mean-time, I'll still crunch for world community grid's projects for humanity.

Out of all of it, my biggest concern in picking a project is ensuring that it's open ... ie: the results are considered public domain, not sequestered away by some business that will patent or copyright it for years to come.

Another World Community Grid cruncher here :-) C4CW is done, Malaria next!

EDIT:

And yes, it does makes me happy. And KIVA.Org too. It made me feel like a part of something big. Its hard where I'm now to actually feel that. And sometimes cost too much money (I still cannot afford a telescope, being a 3rd worlder doing basic stuff paying for apartment and all). But considering I have a PC, I can be a part of a larger grid. Any WCG research done that I'm a part of always makes me happy. No matter the amount of computing days contributed. I would always celebrate it at KFC, alone, being a loner and all. Personally I really wish people working on such numbers and SETI ( while I don't crunch for seti, I did donate and received a digital certificate once) to actually crunch on WCG.

But I also understand that different people is happy for different things. So I guess they have the right to crunch for these numbers and have fun.

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

Very well put. Given finite resources everything we do in research carries an opportunity cost. Maybe it would be better to use those CPU cycles to fold some proteins or whatever. It seems perfectly reasonable to me to ask the question "which of these 3 things is most valuable to do" and do that thing when you can only do one of the three.

Of course the reality is there are 100 things we could do and resources for one, so we can also ask if when we can basically only do a tiny bit at a time if it really matters too much that we do certain things before other things. Given that we can't be sure what will be productive maybe there's some strategy that involves picking a few things almost at random to do and then doing a few other most likely to be useful things, or something. There must be some equivalent of a Nash Equilibrium for this 'game'.

Good point. Pure research--physics and mathematics--is not done because it promises a monetary payback. It is done to satisfy an inner desire to know the truth. Unfortunately--as I have said at another time--all indications are that we have lost our will to pursue truth. As evidenced below...

"...Snark aside, what I'm trying to say is that we (as a species) tend do what pleases us. Great societies arise that harness this tendancy [sic]."---academic.sam

I offer this last is only as a real-life, immediate example of my point: that the only thing that rules today is hedonism: "If it don't feel good and don't put bucks in my pocket, it ain't worth doing".

No one's saying we shouldn't do fundamental research, or pursue things that interest us even if they have no evident application.

The issue is that there are numerous other applications of this kind of processing that will lead to more obvious, more immediate benefits, and it's hard to argue that we should favor searching for large primes instead of, say, helping with protein folding analysis, which leads directly to a better understanding of human biology. It doesn't take much imagination to see how that can lead to medical breakthroughs down the road.

Should we abandon the search for large Mersenne primes? Eh, I guess not. But I won't personally be happy until the balance is severely in favor of (for example) protein folding.

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

I agree with not all scientific curiosity being equally valid, but not with the particular argument. It's inhumanely selfish to believe that just because I am mortal and some scientific research won't lead to amazing things in my lifetime it's not worth pursuing. Sometimes you have to do your part for future generations, just as previous ones did their part for ours even if they didn't enjoy the results. When you are dealing with such generational gaps, you can't be sure if it will pan out or not.

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

People like you are so quick to dismiss the importance of abstract research and theoretical science (like mathematics or theoretical physics). I would be willing to wager that this is primarily because your lack of understanding of the subjects.

These fields are immensely important, and for every dollar invested in science, ten might come out at the end (and a lot of the time, do). Just this economical argument should be enough to illustrate why you should be interested in science. Other than that, I find an existence where all we are concerned about is "practical" things a rather meaningless one. I think that it isn't at all stupid or pointless to spend time in pursuit of knowledge, especially so when history has shown that great use to ordinary lives of ordinary people comes of it. Why should this be less valuable than down-to-earth with consequences that are obvious to you?

In addition, you cannot practically eliminate certain scientific activity which you think won't come to practical use, because as another top comment has illustrated, there were plenty that arose out of whole fields and led to remarkable practical uses (like computers and, for that matter, all of modern civilization).

Additionally, you are making sweeping claims about how the time of humanity should be spent. If you are that concerned with productivity, I recommend cutting all entertainment or pursuit of happiness from your life. To liken theoretical and scientific research to counting grains of sand and to a waste of time when there are so many other things that are, in many more actually measurable ways, affecting society negatively or in much less positive ways is simply absurd.

This kind of science phobia is what got the science budget of the U.S. to be tiny, and the whole nation to be short-sited and uneducated in matters of science.

Very well put. Given finite resources everything we do in research carries an opportunity cost. Maybe it would be better to use those CPU cycles to fold some proteins or whatever. It seems perfectly reasonable to me to ask the question "which of these 3 things is most valuable to do" and do that thing when you can only do one of the three.

That's really not how it works. There isn't a unified "scientific body" optimally distributing scientific efforts. If it were obvious how to do this, the world would be a much simpler place. That is the whole point of exploring and venturing into the unknown. Plus, it takes time and effort to set up different algorithms, and people have limited time!

Thanks for writing this article, Casey. I had not realized previously that you had a degree in applied physics. Many of us enjoy these types of articles discussing latest physics or math developments, even though we may not have degrees to provide a foundation of knowledge in the area. We appreciate the breakdown such as provided here. Keep it up!

The one thing I don't like about all these "we should do it because it may be useful someday" arguments is that it ignores the fact that we're mortal and have limited resources on our planet. Of course anything could eventually be useful, but we need to prioritize our time and computers for things that we think are more likely to lead us somewhere. Might we guess wrong? Sure, but that's the nature of our limited, non-godlike existence.

I could decide to spend my whole life counting the grains of sand in Florida, but what are the odds that that would eventually be useful vs. the odds that I'd just waste my life?

This is not me arguing against prime numbers, by the way (which Casey made some interesting points for), but against the attitude that says all scientific curiosity is equally valid. Until we become immortal that argument can't work. Whenever we choose to study something we are choosing to NOT study something else, so the conversation over "why do this?" will always be a useful one.

This is an interesting point, but consider this.

There are over 6 billion human beings on the planet. A healthy percentage of them are engaged in the process of studying something.

As a species, we are studying pretty much everything of worth in all directions simultaneously. Given this vast amount of time, and the potential benefits of an unintended discovery, why not spend some small fraction of this resource studying something that doesn't appear to have an immediate impact?